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Solve for X. Leave your answer in the simplest radical form.
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Solve For X Leave Your Answer In The Simplest Radical Form Image Down Below Someone Please Help Me With This Ill Give You Brainlist And Points class=

Sagot :

Apply Pythagorean theorem

  • P²=10²-4²
  • P²=100-16
  • P²=84
  • p=2√21

Again

  • x²=84-8²
  • x²=84-64
  • x²=20
  • x≈√20=√4×5=2√5
Nayefx

Answer:

2√5

Step-by-step explanation:

The given pyramid is composed of two right angle triangles. Notice the triangles of the pyramid share a common side. With the help of it, we can figure out x

recall Pythagoras theorem

[tex] {a}^{2} + { b }^{2} = {c}^{2} [/tex]

Case-1: Finding the opposite side

here,

  • a=4
  • c=10

To find:

  • b

now plug in the value of a and c in the formula respectively:

[tex] {4}^{2} + { b }^{2} = {10}^{2} \\ \implies {b}^{2} = {10}^{2} - {4}^{2} \\ \implies {b}^{2} = 84 \\ \implies \boxed{ b_{1} = 2\sqrt{21}}[/tex]

Case-2: Finding x

here,

  • [tex]b_1 \implies c=2\sqrt{21}[/tex]
  • b=8
  • a[tex]\implies[/tex] x

Utilizing Pythagoras theorem yields:

[tex] {x}^{2} + { 8}^{2} = {(2\sqrt{21})}^{2} \\ \implies {x}^{2} = {(2\sqrt{21})}^{2} - {8}^{2} \\ \implies {x}^{2} = 20\\ \implies \boxed{ x= 2\sqrt{5}}[/tex]

and we're done!